Yes, there is a laundry room at Kidani. I did not used it last time as when I had time, all the washers where taken (I believe there is only 3). It is located near the Arcade in the corridor nearest to the Souvenir shop.
From the lobby head to community hall, they are on the right after the elevators (left) and the ATM and mailbox (right), continue and they will be on your right before you get to the corridor to WDW transportion. If you reach the last you have gone to far.